I had a similar bizarre problem with my 66 Lemans with an HD 3spd and LSD. When I would roll it out of the garage it would occasionally give a big thud from the rear. It would also sometimes do it while turning at very low speeds such as in a parking lot. I suspected brake binding in the rear or a diff issue but couldn't find anything. Long story short, what it needed was GM limited slip diff additive. I had apparently forgotten to add it though I thought I had during a 4'wheel disc brake conversion. Drained the diff, added the additive and filled with new diff lube. Problem solved.
Without the limited slip additive, the limited slip friction clutches have too much bite and the thud is them being forced to release. At road speed everything is happening so fast and normal road vibration masks the symptoms so you don't hear it. I have been advised over the years to only use factory GM LSD additive and whatever diff lube you want.
As to the look of the driveshaft, the eye can play tricks on you and give the appearance of out of round. Ever seen a dirty tire/wheel look out of round on another car on the highway? As someone else said, it would get worse with speed or at least show up at the same speed consistently due to harmonics.
As far as the two wheels appearing to turn at different speeds on the lift, that is right, they will be different. Remember this is "limited slip" not a locker. Unloaded the amount of friction in the diff is small and the viscous coupling won't generate enough heat to equalize the rotational speed.
Try redoing the lube and put the GM LSD lube in first to make sure you have put in enough. I don't remember how much you need but that shouldn't be hard to find. It's an inexpensive thing to try before you spend a fortune. Just an idea.
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